76.5.29 problem 30

Internal problem ID [17378]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 30
Date solved : Monday, March 31, 2025 at 04:10:31 PM
CAS classification : [_separable]

\begin{align*} 5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=5*x*y(x)^2+5*y(x)+(5*x^2*y(x)+5*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {1}{x} \\ y &= \frac {-5-c_1}{5 x} \\ y &= \frac {-5+c_1}{5 x} \\ \end{align*}

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 29

ode=(5*x*y[x]^2+5*y[x])+(5*x^2*y[x]+5*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {1}{x} \\ y(x)\to \frac {c_1}{x} \\ y(x)\to -\frac {1}{x} \\ \end{align*}

✓ Sympy. Time used: 0.171 (sec). Leaf size: 5

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*x*y(x)**2 + (5*x**2*y(x) + 5*x)*Derivative(y(x), x) + 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} \]